Geodesic
Inequivalence of difference sets: on a remark of Baumert
Padraig Ó Catháin1
1University of Queensland
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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An often cited statement of Baumert in his book Cyclic difference sets asserts that four well known families of cyclic $(4t-1,2t-1,t-1)$ difference sets are inequivalent, apart from a small number of exceptions with $t< 8$. We are not aware of a proof of this statement in the literature.Three of the families discussed by Baumert have analogous constructions in non-cyclic groups. We extend his inequivalence statement to a general inequivalence result, for which we provide a complete and self-contained proof. We preface our proof with a survey of the four families of difference sets, since there seems to be some confusion in the literature between the cyclic and non-cyclic cases.
DOI : 10.37236/2277
Classification : 05B10, 05B20
Mots-clés : difference sets, Hadamard matrices

Padraig Ó Catháin  1

1 University of Queensland 
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Padraig Ó Catháin. Inequivalence of difference sets: on a remark of Baumert. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2277

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